Direct sum of group representations

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created: 2021-12-03 01:24:50
modified: 2022-01-13 14:39:46

Consider a group and two representations and .

The direct sum of the representations is and for finite dimensional vector spaces, is given by:

Meant in a matrix block form. This is the same as the direct sum of matrices. is the direct sum of the vector spaces and .

Here, and are both sub-representations of . ^abb55c